TSTP Solution File: NUN073+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:51:02 EDT 2023
% Result : Theorem 5.47s 1.47s
% Output : Proof 6.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 09:40:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.63/1.05 Prover 4: Preprocessing ...
% 2.63/1.05 Prover 1: Preprocessing ...
% 2.63/1.09 Prover 6: Preprocessing ...
% 2.63/1.09 Prover 2: Preprocessing ...
% 2.63/1.09 Prover 0: Preprocessing ...
% 2.63/1.09 Prover 3: Preprocessing ...
% 2.63/1.09 Prover 5: Preprocessing ...
% 4.56/1.31 Prover 1: Warning: ignoring some quantifiers
% 4.56/1.33 Prover 4: Warning: ignoring some quantifiers
% 4.56/1.33 Prover 1: Constructing countermodel ...
% 4.56/1.33 Prover 6: Proving ...
% 4.56/1.33 Prover 5: Proving ...
% 4.56/1.33 Prover 2: Proving ...
% 4.56/1.35 Prover 3: Warning: ignoring some quantifiers
% 4.56/1.35 Prover 4: Constructing countermodel ...
% 4.56/1.36 Prover 3: Constructing countermodel ...
% 4.56/1.36 Prover 0: Proving ...
% 5.47/1.47 Prover 0: proved (838ms)
% 5.47/1.47
% 5.47/1.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.47
% 5.47/1.48 Prover 2: proved (839ms)
% 5.47/1.48
% 5.47/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.48
% 5.47/1.48 Prover 6: stopped
% 5.47/1.48 Prover 5: stopped
% 5.47/1.48 Prover 4: Found proof (size 13)
% 5.47/1.48 Prover 3: stopped
% 5.47/1.48 Prover 4: proved (837ms)
% 5.47/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.47/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.47/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.47/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.47/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.47/1.50 Prover 1: stopped
% 6.07/1.53 Prover 10: Preprocessing ...
% 6.07/1.53 Prover 11: Preprocessing ...
% 6.07/1.54 Prover 7: Preprocessing ...
% 6.07/1.54 Prover 13: Preprocessing ...
% 6.07/1.55 Prover 8: Preprocessing ...
% 6.07/1.55 Prover 10: stopped
% 6.07/1.55 Prover 7: stopped
% 6.07/1.56 Prover 13: stopped
% 6.07/1.56 Prover 11: stopped
% 6.51/1.61 Prover 8: Warning: ignoring some quantifiers
% 6.51/1.62 Prover 8: Constructing countermodel ...
% 6.51/1.62 Prover 8: stopped
% 6.51/1.62
% 6.51/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.51/1.63
% 6.51/1.63 % SZS output start Proof for theBenchmark
% 6.51/1.63 Assumptions after simplification:
% 6.51/1.63 ---------------------------------
% 6.51/1.63
% 6.51/1.63 (axiom_1)
% 6.51/1.66 ? [v0: $i] : ($i(v0) & ! [v1: $i] : (v1 = v0 | ~ (r1(v1) = 0) | ~ $i(v1))
% 6.51/1.66 & ! [v1: int] : (v1 = 0 | ~ (r1(v0) = v1)))
% 6.51/1.66
% 6.51/1.66 (axiom_3a)
% 6.51/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (r2(v1, v2) = 0) | ~
% 6.51/1.66 (r2(v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 6.51/1.66
% 6.51/1.66 (axiom_7a)
% 6.51/1.66 ! [v0: $i] : ! [v1: $i] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0) | ~ $i(v1)
% 6.51/1.66 | ~ $i(v0))
% 6.51/1.66
% 6.51/1.66 (oneuneqtwo)
% 6.51/1.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (r2(v3, v0) = 0 &
% 6.51/1.66 r2(v2, v1) = 0 & r2(v1, v0) = 0 & r1(v3) = 0 & r1(v2) = 0 & $i(v3) & $i(v2)
% 6.51/1.66 & $i(v1) & $i(v0))
% 6.51/1.66
% 6.51/1.66 Further assumptions not needed in the proof:
% 6.51/1.66 --------------------------------------------
% 6.51/1.66 axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_4, axiom_4a, axiom_5a, axiom_6a
% 6.51/1.66
% 6.51/1.66 Those formulas are unsatisfiable:
% 6.51/1.66 ---------------------------------
% 6.51/1.66
% 6.51/1.66 Begin of proof
% 6.90/1.66 |
% 6.90/1.67 | DELTA: instantiating (axiom_1) with fresh symbol all_6_0 gives:
% 6.90/1.67 | (1) $i(all_6_0) & ! [v0: any] : (v0 = all_6_0 | ~ (r1(v0) = 0) | ~
% 6.90/1.67 | $i(v0)) & ! [v0: int] : (v0 = 0 | ~ (r1(all_6_0) = v0))
% 6.90/1.67 |
% 6.90/1.67 | ALPHA: (1) implies:
% 6.90/1.67 | (2) ! [v0: any] : (v0 = all_6_0 | ~ (r1(v0) = 0) | ~ $i(v0))
% 6.90/1.67 |
% 6.90/1.67 | DELTA: instantiating (oneuneqtwo) with fresh symbols all_13_0, all_13_1,
% 6.90/1.67 | all_13_2, all_13_3 gives:
% 6.90/1.67 | (3) r2(all_13_0, all_13_3) = 0 & r2(all_13_1, all_13_2) = 0 & r2(all_13_2,
% 6.90/1.67 | all_13_3) = 0 & r1(all_13_0) = 0 & r1(all_13_1) = 0 & $i(all_13_0) &
% 6.90/1.67 | $i(all_13_1) & $i(all_13_2) & $i(all_13_3)
% 6.90/1.67 |
% 6.90/1.67 | ALPHA: (3) implies:
% 6.90/1.67 | (4) $i(all_13_3)
% 6.90/1.67 | (5) $i(all_13_2)
% 6.90/1.67 | (6) $i(all_13_1)
% 6.90/1.67 | (7) $i(all_13_0)
% 6.90/1.67 | (8) r1(all_13_1) = 0
% 6.90/1.67 | (9) r1(all_13_0) = 0
% 6.90/1.67 | (10) r2(all_13_2, all_13_3) = 0
% 6.90/1.67 | (11) r2(all_13_1, all_13_2) = 0
% 6.90/1.67 | (12) r2(all_13_0, all_13_3) = 0
% 6.90/1.67 |
% 6.95/1.68 | GROUND_INST: instantiating (2) with all_13_1, simplifying with (6), (8) gives:
% 6.95/1.68 | (13) all_13_1 = all_6_0
% 6.95/1.68 |
% 6.95/1.68 | GROUND_INST: instantiating (2) with all_13_0, simplifying with (7), (9) gives:
% 6.95/1.68 | (14) all_13_0 = all_6_0
% 6.95/1.68 |
% 6.95/1.68 | GROUND_INST: instantiating (axiom_3a) with all_13_2, all_13_0, all_13_3,
% 6.95/1.68 | simplifying with (4), (5), (7), (10), (12) gives:
% 6.95/1.68 | (15) all_13_0 = all_13_2
% 6.95/1.68 |
% 6.95/1.68 | COMBINE_EQS: (14), (15) imply:
% 6.95/1.68 | (16) all_13_2 = all_6_0
% 6.95/1.68 |
% 6.95/1.68 | REDUCE: (11), (13), (16) imply:
% 6.95/1.68 | (17) r2(all_6_0, all_6_0) = 0
% 6.95/1.68 |
% 6.95/1.68 | REDUCE: (8), (13) imply:
% 6.95/1.68 | (18) r1(all_6_0) = 0
% 6.95/1.68 |
% 6.95/1.68 | REDUCE: (5), (16) imply:
% 6.95/1.68 | (19) $i(all_6_0)
% 6.95/1.68 |
% 6.95/1.68 | GROUND_INST: instantiating (axiom_7a) with all_6_0, all_6_0, simplifying with
% 6.95/1.68 | (17), (18), (19) gives:
% 6.95/1.68 | (20) $false
% 6.95/1.68 |
% 6.95/1.68 | CLOSE: (20) is inconsistent.
% 6.95/1.68 |
% 6.95/1.68 End of proof
% 6.95/1.68 % SZS output end Proof for theBenchmark
% 6.95/1.68
% 6.95/1.68 1067ms
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